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POST UTME IGBINEDION UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ about the x-axis.

Correct A. $\frac{32\pi}{3}$\)

B. $\frac{64\pi}{3}$\)

C. $\frac{128\pi}{3}$\)

D. $\frac{256\pi}{3}$\)

Correct Answer: A

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Question 2 View Details

If u = \$\sin^3$ x, find $\frac{du}{dx}$\) using the chain rule.

Correct A. 3\$\sin^2$ x \cos x

B. \cos x

C. \sin x

D. \$\cos^3$ x

Correct Answer: A

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Question 3 View Details

Find the sum of the first 10 terms of the geometric series 2 + 6 + 18 + ...

A. 104

B. 106

Correct C. 108

D. 110

Correct Answer: C

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Question 4 View Details

Solve the system of equations using matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}

Correct A. $x = 1$, $y = 2$

B. $x = 2$, $y = 1$

C. $x = 3$, $y = 4$

D. $x = 4$, $y = 3$

Correct Answer: A

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Question 5 View Details

Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 6 View Details

Let $S = {1, 2, 3, 4, 5}$ be a set of integers. Find the number of subsets of ( S ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 7 View Details

Find the sum of the first 10 terms of the arithmetic sequence ( 2, 5, 8, ldots ).

A. 50

B. 55

Correct C. 60

D. 65

Correct Answer: C

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Question 8 View Details

The polynomial ( P(x) = $x^3 - 6x^2 + 11x - 6$ ) has a root at $x = 1$. Find the other two roots.

Correct A. 2, 3

B. 3, 4

C. 4, 5

D. 5, 6

Correct Answer: A

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Question 9 View Details

The mean of the numbers 2, 4, 6, 8, and 10 is 6. Find the mean of the numbers 3, 5, 7, 9, and 11.

A. 7

Correct B. 8

C. 9

D. 10

Correct Answer: B

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Question 10 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 4$.

A. 16

B. 20

Correct C. 24

D. 28

Correct Answer: C

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Question 11 View Details

Determine the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{5}$\) ).

Correct A. $\frac{\pi}{4}$

B. $\frac{\pi}{3}$

C. $\frac{\pi}{2}$

D. $\frac{\pi}{6}$

Correct Answer: A

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Question 12 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using the chain rule.

Correct A. ( f'$(x) =$$\frac{-2x}{x^2 + 1$ ^2}\)\) )

B. ( f'$(x) =$$\frac{2x}{x^2 + 1$ ^2}\)\) )

C. ( f'$(x) =$$\frac{2}{x^2 + 1$ ^2}\)\) )

D. ( f'$(x) =$$\frac{-2}{x^2 + 1$ ^2}\)\) )

Correct Answer: A

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Question 13 View Details

Solve the inequality $2^x > 10$ using \logarithms.

Correct A. $x > 3.3219$

B. $x < 3.3219$

C. $x > 1.5$

D. $x < 1.5$

Correct Answer: A

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Question 14 View Details

Determine the value of $\sqrt[3]{64}$ using the properties of exponents.

Correct A. ( 4 )

B. ( 8 )

C. ( 16 )

D. ( 32 )

Correct Answer: A

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Question 15 View Details

Find the probability of drawing two hearts from a standard deck of 52 cards.

Correct A. $\frac{1}{221}$

B. $\frac{1}{52}$

C. $\frac{1}{26}$

D. $\frac{1}{13}$

Correct Answer: A

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Question 16 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 2$ from $x = 0$ to $x = 4$.

Correct A. $\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4$

B. $\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 + \frac{1}{2}$

C. $\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 - \frac{1}{2}$

D. $\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4$

Correct Answer: A

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Question 17 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If 75% of the scores fall below 70, what is the z-score corresponding to a score of 70?

A. 0.5

Correct B. 1

C. 1.25

D. 1.5

Correct Answer: B

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Question 18 View Details

Solve the quadratic equation $x^2 + 4x - 5 = 0$.

Correct A. $x = -5, x = 1$

B. $x = -1, x = 5$

C. $x = -2, x = 2.5$

D. $x = -1, x = 5$

Correct Answer: A

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Question 19 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. $\frac{1}{2}$

Correct B. $\frac{3}{8}$

C. $\frac{1}{4}$

D. $\frac{3}{5}$

Correct Answer: B

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Question 20 View Details

Find the sum of the first 5 terms of the geometric sequence ( 2, 6, 18, ... ).

Correct A. ( 62 )

B. ( 64 )

C. ( 66 )

D. ( 68 )

Correct Answer: A

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Question 21 View Details

Let X and Y be independent random variables with probability density functions f_$X(x) = 2x$, $0 < x$$< 1$, and f_$Y(y) =$$3y^2$,$(0 < y$\) < 1. Find the probability that $X + Y < 1\\((0 < y) < 1. Find the probability that$.

A. $1/4$

B. $1/2$

Correct C. $3/4$

D. 1

Correct Answer: C

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Question 22 View Details

Find the determinant of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 23 View Details

Let $\vec{a} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and $\vec{b} = \begin{bmatrix} 3 \\ 4 end{bmatrix}$. Find the dot product of $\\(end{bmatrix}). Find the dot product of \vec{a}$ and $\vec{b}$.

A. 11

Correct B. 12

C. 13

D. 14

Correct Answer: B

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Question 24 View Details

Simplify the expression $\frac{2^3 \cdot 3^2}{2^2 \cdot 3}$.

A. 4

B. 6

Correct C. 8

D. 12

Correct Answer: C

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Question 25 View Details

Find the value of $\log_{10} (100)$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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